A perfect lens focuses light to a single point on an optical axis of the lens. An aberration of the lens of an eye is a deviation from the perfect focusing of light due to a distortion of a wavefront of light as it passes through the eye having irregularities. The distortion of a wavefront of light may be referred to as an aberrated wavefront. Conventional aberrations of the eye consist of spherical de-focus and regular astigmatism (cylinder), which are correctable by conventional ophthalmic lenses. An eye may also have higher order aberrations, such as, spherical aberration, trefoil, irregular astigmatism, and coma. Each higher order aberration may be represented mathematically by a basis set of polynomials of degree three or more. For example, the aberrations of trefoil and coma are typically represented by third-order polynomials, while the aberration of spherical aberration is typically represented by fourth-order polynomials with respect to radius. With respect to azimuth angle, θ, the aberration wavefront of spherical aberration is represented by a zero-order polynomial, which is constant for all azimuth angles at each radius. That is, the aberration wavefront of spherical aberration is rotationally symmetric, which makes this particular higher order aberration of special interest for further discussion here.
The aberration wavefronts of spherical aberrations of the eye are commonly described mathematically using a series of Zernike polynomials. The Zernike term, Z∘4, for spherical aberration of the eye is typically of the form:Z∘4=ar4−br2  (1)where r is the normalized radial position within the pupil measured from the optical axis of the eye and a and b are constants. An alternate mathematical representation of spherical aberration, referred to as the ‘Seidel representation’, is of the form, ar4. The Zernike term, ar4, is referred to as the spherical aberration term and the Zernike term, br2, is referred to as the quadratic spherical de-focusing term. Other mathematical representations of spherical aberration of the eye are known, depending on the basis set chosen.
FIG. 1 is a graph of equation (1) showing a spherical aberration wavefront using the Zernike basis set representation. Spherical aberration of the eye can be positive or negative, or zero for example at zero radius.
A variety of approaches are typically used to correct spherical aberration of the eye. One approach exploits the aforementioned rotational symmetry of spherical aberration. In this approach, a lens for correcting spherical aberration is also rotationally symmetric. Such a lens may have a radially symmetric optical power or optical phase variation that is equal and opposite (or nearly so) to that of the aberrated eye. The lens effectively cancels the spherical aberration of the eye. The spherical aberration correction of a lens can be positive (for canceling a negative spherical aberration of the eye) or negative (for canceling a positive spherical aberration of the eye). Although a lens for correcting a fixed amount of spherical aberration is known, other problems arise.
It is shown in equation (1) and FIG. 1 that the amount of distortion (de-focus) of an image due to spherical aberration of an eye depends on the radius of its pupil. Thus, as the pupil changes in size (e.g., in response to a change in ambient light), the amount of spherical aberration affecting de-focus in the eye changes accordingly. This relationship is shown in FIGS. 2-5, which show side views of the focusing of light by a lens 95 of an eye having differently sized openings or pupils.
FIG. 2 shows the lens 95 having a pupil dilated to its maximum diameter (i.e., there is no pupil present to obstruct light). The lens focuses light rays 50, 60, and 70, to multiple points 55, 65, and 75, respectively, on an optic axis of the lens. These multiple focal points are the result of spherical aberration of the natural lens of the eye. It is to be understood that FIGS. 2-5 show the focal points of a few discrete rays and that in an actual optical system there is a continuum of focal points between the focal point 55 and the focal point 75, inclusive of the focal point 65.
FIGS. 3-5 show the lens 95 having pupils 90, 85, and 80, respectively, with respectively decreasing diameter. FIGS. 3-5 show that as the pupil diameter decreases, the multiplicity of focus points (i.e., the degree and effects of spherical aberration) decreases as well. The lens of FIG. 3, having the pupil 90 with the relatively largest diameter, focuses the light rays 50, 60, and 70, to the largest number of distinct points 55, 65, and 75, respectively, on the optic axis of the lens. The lens of FIG. 4, having the pupil 85 with the relatively mid-range diameter, focuses the light rays to a relatively mid-range number of points 55 and 65 (between the numbers in FIGS. 3 and 5) on an optic axis of the eye lens. The lens of FIG. 5, having the pupil 80 with the relatively smallest diameter, focuses the light rays to the smallest number (one) point 55 on an optic axis of the eye lens.
It may be observed that as the diameter of the pupil changes, e.g., with changing ambient light, the amount of the spherical aberration of the natural lens of the eye that is revealed is likewise changed. The amount of spherical aberration that is revealed in the eye typically affects the optical quality of the eye. It is also known that as the diameter of the pupil changes, other higher order aberrations of the eye, such as trefoil may affect image quality as well. While a conventional lens may correct for a fixed amount of spherical aberration and/or other higher order aberrations, a fixed lens cannot provide the necessary correction for changing aberrations in the eye.
There is therefore a great need in the art for providing a lens for providing correction for higher order aberrations in the eye, such as spherical aberration, trefoil, irregular astigmatism, and coma, that change the phase correction profile in response to a change in ambient light or pupil diameter. Accordingly, there is now provided with this invention an improved lens for effectively overcoming the aforementioned difficulties and longstanding problems inherent in the art.